Question

Given the equation $y=\frac{x+7a}{x-a^2}$. What is $x$ in terms of $y$ and $a$?

• A. $x=\frac{y+7a}{y-a^2}$
• B. $x=\frac{y+7a}{y{a}^2}$
• C. $x=\frac{y{a}^2+7a}{y-1}$
• D. $x=y(a^2+7a)$
• E. $x=(y+7a)(y-a^2)$

Answer 1

The correct option is C $x=\frac{y{a}^2+7a}{y-1}$

Given equation is $y=\frac{x+7a}{x-a^2}$

$\Rightarrow y(x-a^2)=x+7a\Rightarrow yx-a^{2}y=x+7a\Rightarrow xy-x=7a+a^{2}y\Rightarrow x(y-1)=7a+a^{2}y\Rightarrow x=\frac{y{a}^2+7a}{y-1}$